adjoin_algebraMap — Mathlib

English

For a map of algebras algebra S → A, adjoin of the image of s under algebraMap S A equals the range of the induced map plus adjoin of s, i.e., adjoin R (algebraMap S A '' s) = range ⊔ adjoin R s.

Русский

Для отображения алгебр algebraMap S A образ s образует адъюнкт: adjoin R (algebraMap S A '' s) = range ⊔ adjoin R s.

LaTeX

$$$ adjoin\ R (algebraMap S A '' s) = (IsScalarTower.toAlgHom R S A).range \u2223\ uplus adjoin R s $$$

Lean4

theorem adjoin_algebraMap (s : Set S) :
    adjoin R (algebraMap S A '' s) = (adjoin R s).map (IsScalarTower.toAlgHom R S A) :=
  adjoin_image R (IsScalarTower.toAlgHom R S A) s

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